3.01 – Review of 3.01 – Review of LinesLines

3.01 – Review of 3.01 – Review of LinesLines

Flashing Back to Grade 10Flashing Back to Grade 10

Goals for this Mini-Unit• Be able to find the equation of a

line through two points• Know how parallel and

perpendicular lines are related• Find the intersection of lines• Prove that line segments form

certain geometric shapes

Goals for this Mini-Unit

• Relate line segments to chords of circles

• Find the centre of a circle• Find the radius of a circle• Apply the distance and midpoint

formulae in circles

Review of Lines• Every straight line follows the

equation y = mx + b• m is the slope – a measure of how

steep the line is• m = rise = Δ y run Δ x• b is the y-intercept

Finding the Eq’n of a Line

• If a line has a slope of -3 and passes through the point (8, 1), what is its equation?

• y = -3x + b• 1 = -3(8) + b• 1 = -24 + b b = 25• y = -3x + 25

Finding the Eq’n of a Line

• A line passes through the points (3, 2) and (9, 12). Find its equation.

3

52

)3(3

52

3

53

5

6

10

39

212

b

b

b

bxy

m

33

5 xy

Working with Slopes• The symbol || means ‘parallel’• Parallel lines are always the same

distance apart; they never touch; their equations have the same slope

• The lines y = 2x + 10 and y = 2x – 5 are parallel – we can tell because they both have a slope of 2.

Working with Slopes• The symbol ┴ means ‘perpendicular’• Perpendicular lines intersect (cross) at

right angles; their equations have slopes which are negative reciprocals

• The lines y = ¼x – 20 and y = -4x + 1 are perpendicular, because ¼ and -4 are negative reciprocals of each other.

A Note on Naming• Typically in this unit we will be dealing

with line segments rather than lines. These are distinguished by putting a line over the two letters representing its endpoints.

• Often you will find several slopes – use subscripts to keep them identified.

Example• Refer to p. 222 of the textbook – we

are going to do #1 as an example.

• Our first step is to plot GOLD to see which sides ought to be parallel, and which are perpendicular.

6

4

2

-2

-4

-6

-8

-10

-12

-10 -5 5 10 15

G

O

L

D

Example• We expect GO to be parallel to LD

5

125

1238

66

GO

GO

GO

m

m

m

5

1249

111

LD

LD

m

m

Same slope, they are parallel

Example• We also expect OL to be parallel to

GD.

12

512

593

16

OL

OL

OL

m

m

m

12

548

116

GD

GD

m

m

Same slope, they are parallel

Example• In finding these 4 slopes, we can also

show that adjacent sides are perpendicular.

• is the negative reciprocal of

• Adjacent sides are therefore ┴

5

1212

5